Modified Hamiltonian-driven shortest-path ray tracing in dissipative anisotropic media

Abstract

Enhancing ray tracing in dissipative anisotropic media is challenging because the subsurface exhibits both geologic and rheological discontinuities and directionally dependent attenuation. Conventional real-ray tracing and complex energy-velocity formulations struggle with qSV cusps, wavefront triplications, and abrupt discontinuities. Recent conjugate and shortest-path extensions have been proposed to mitigate these issues, yet they rely on approximate Hamiltonian formulations that are typically tested in smooth background models. In addition, they rarely address first-arrival refraction or the coupled behavior of wave propagation and energy dissipation. Here, the g*-Hamiltonian-based formulation is incorporated into a shortest-path-based ray-tracing algorithm for layered dissipative anisotropic media. At the local scale, we first compute the complex energy velocities and corresponding ray quantities, which are ray velocity, ray attenuation, and ray quality factor, using three kernels. These kernels produce complex energy velocities for all body waves in different fashions, namely, the original complex energy velocity (OEV), conjugate real ray tracing (C-RRT), and g*-Hamiltonian (MEV). We then analyze their discrepancies and numerical behavior and examine several optimization strategies. The results demonstrate that all kernels agree for qSH and qP waves, whereas OEV generates pseudo-reflection or numerical instability and unphysical attenuation along ray paths in qSV modeling. C-RRT produces large errors, including non-physical negative attenuation in some qP and qSV traveltime values, and strongly biased ray quality factors under our parameter regime. Among the tested kernels, MEV-driven shortest-path ray tracing produces the most computationally stable first-arrival behavior.